MOVED: Warm Places in Europe in January

I am interested in booking a flight to Europe in January 2014. I basically can redeem 35,000 US Airways miles to fly round-trip from the US to Europe in January or February. I need to know if there is a group of islands or some region that is warm that time of year. Ideally I'd like a little beach time.

Is there any place that gets warm in Europe during January/February? Any help would be much appreciated!